Lectures related to Transcritical Bifurcation in Dynamical Systems

Dynamical Systems: Equilibrium Points and Stability

Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.

Dynamical Systems: Maps and Stability

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Introduction to Dynamical System

Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.

Bifurcations: Fold Bifurcation

Covers the concept of fold bifurcation in dynamical systems, focusing on the saddle-mode behavior.

Transcritical Bifurcation: Theory and Applications

Explores the theory and applications of transcritical bifurcation, focusing on stability analysis and critical points.

Bifurcations: Flip and Andronov-Hopf

Explores flip and Andronov-Hopf bifurcations, showing how systems change equilibrium points and stability.

Mathematical Modeling in Chemistry and Biology

Covers mathematical modeling in chemistry and biology, including chemical reactions, enzymatic kinetics, and population dynamics.

Stochastic Models: Absorbing Markov Chains Examples

Covers examples of absorbing Markov chains in discrete time.

Dynamical System Theory for Engineers

Introduces dynamical system theory for engineers, covering system behavior, stability, and mathematical applications.

Introduction to Dynamical System Theory for Engineers

Covers trajectory, solution, and orbit of dynamical systems for engineers.

Dynamical Systems for Engineers

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Small Scale Stability: Gradient Systems

Explores small scale stability in gradient systems, analyzing trajectories and attractors in phase space.

Bifurcations: Introduction

Covers the introduction to bifurcations in dynamical systems, including examples and theorems.

Chaos and Lyapunov Exponents: Analyzing Predictability

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Attractors and Stability

Explores attractors and their stability in dynamical systems, including fixed points, periodic orbits, and chaotic attractors.

Dynamical System Theory: Bifurcations

Covers the topic of bifurcations in dynamical system theory, focusing on the pitchfork bifurcation.

Dynamic Systems: Formalism and Bases

Covers the formalism and bases of dynamic systems, including differential equations and non-linear systems.

Transcritical Bifurcation: SIS Epidemics

Explores transcritical bifurcation in SIS epidemics, analyzing mathematical equations and system dynamics.

Learning Chemical Reaction Networks

Explores sparse learning of chemical reaction networks from trajectory data using data-based methods and learning approaches.